Question

A particle of mass m moving with a velocity v collides with a particle of mass 2m at rest and sticks to it. Velocity of the combined mass equal to? 

• A. v
• B. \(\frac{v}{2}\)
• C. \(\frac{v}{3}\)
• D. \(\frac{v}{4}\)

Answer 1

The Correct Option is C

 

Calculation of Final Velocity After Collision:

Given Data:

• Mass of first particle: \( m_1 = m \)
• Mass of second particle: \( m_2 = 2m \)
• Initial velocity of first particle: \( v_1 = v \)
• Initial velocity of second particle: \( v_2 = 0 \) (at rest)

Step 1: Initial Momentum of the System

The initial momentum is:

\[ p_i = m_1v_1 + m_2v_2 = mv + 0 = mv \]

Step 2: Final Momentum of the System

After the collision, both particles stick together, forming a combined mass:

\[ m_{\text{combined}} = m_1 + m_2 = m + 2m = 3m \]

Let \( V \) be the velocity of the combined mass. The final momentum is:

\[ p_f = (m_1 + m_2)V = 3mV \]

Step 3: Conservation of Momentum

Using the law of conservation of momentum:

\[ p_i = p_f \]

Substitute the values:

\[ mv = 3mV \]

Solve for \( V \):

\[ V = \frac{v}{3} \]

Conclusion:

The final velocity of the combined mass is \( \frac{v}{3} \).

Answer: C